Question

-1. The table shows the annual consumption of cheese per person in the United States for selected years in the 20th century. Let x = number of years since 1900, and y = pounds per person.

Year Pounds Consumed
1912 4.976
1932 8.717
1969 16.997
1979 21.705

What cubic model best fits this data?

-2. The table shows the annual consumption of cheese per person in the U.S. for selected years in the 20th century.

Year Pounds Consumed
1913 4.468
1926 5.56
1955 4.778
1990 10.905

Use a cubic model to estimate milk production in 1989.
a. 20.9
b. 10.5
c. 14.5
d. 6.5

-3. Use synthetic division to find P(-1) for P(x)=x^4+x^3+4x^2-10x+4
a. -1
b. -16
c. 18
d. 8

Answer 1

Using processing software (Excel) or even a decent scientific calculator. You input the values and generate the best fit cubic equation.
For number 1, the equation is
y = 8x10⁻⁵ x³ - 0.0097 x² + 0.374 x + 1.083
where x is the number of years since 1900
y is the pounds cheese consumed

For number 2, the equation is
y = -3x10⁻⁵ x³ + 0.0028 x² + 0.2155 x + 1.7736

For number 3
P(-1) = 18